The rapid acceleration of global urbanization has introduced novel challenges in enhancing urban infrastructure and services. Spatio-temporal data, integrating spatial and temporal dimensions, has emerged as a critical tool for understanding urban phenomena and promoting sustainability. In this context, Federated Learning (FL) has gained prominence as a distributed learning paradigm aligned with the privacy requirements of urban IoT environments. However, integrating traditional and deep learning models into the FL framework poses significant challenges, particularly in capturing complex spatio-temporal dependencies and adapting to diverse urban conditions. To address these challenges, we propose the Federated Local Data-Infused Graph Creation with Node-centric Model Refinement (Fed-LDR) algorithm. Fed-LDR leverages FL and Graph Convolutional Networks (GCN) to enhance spatio-temporal data analysis in urban environments. The algorithm comprises two key modules: (1) the Local Data-Infused Graph Creation (LDIGC) module, which dynamically reconfigures adjacency matrices to reflect evolving spatial relationships within urban environments, and (2) the Node-centric Model Refinement (NoMoR) module, which customizes model parameters for individual urban nodes to accommodate heterogeneity. Evaluations on the PeMSD4 and PeMSD8 datasets demonstrate Fed-LDR's superior performance over six baseline methods. Fed-LDR achieved the lowest Mean Absolute Error (MAE) values of 20.15 and 17.30, and the lowest Root Mean Square Error (RMSE) values of 32.30 and 27.15, respectively, while maintaining a high correlation coefficient of 0.96 across both datasets. Notably, on the PeMSD4 dataset, Fed-LDR reduced MAE and RMSE by up to 81\% and 78\%, respectively, compared to the best-performing baseline FedMedian.